By Holtje, Hans-Dieter
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Additional resources for A Chemists Guide to Density Functional Theory
This interaction depends on the distance between two electrons weighted by the probability that this distance will occur. , where we have integrated over the spin coordinates) which contains just this information Eee = Ψ N N 1 ∑∑ r i j > i ij Ψ = r r 1 ρ2 (r1 , r2 ) r r dr1dr2 . 2 ∫ ∫ r12 (2-18) r r r r r r r Using ρ 2 ( r1 , r2 ) = ρ( r1 )ρ( r2 ) + ρ( r1 )h XC ( r1; r2 ) (cf. 3 Fermi and Coulomb Holes E ee 1 = 2 r r ρ( r1 )ρ( r2 ) r r 1 ∫ ∫ r12 dr1dr2 + 2 r r r ρ( r1 )h XC ( r1; r2 ) r r d r1dr2 .
A, 101, 5390 (1997), with permission by the American Chemical Society). 28 A Chemist’s Guide to Density Functional Theory. Second Edition Wolfram Koch, Max C. Holthausen Copyright © 2001 Wiley-VCH Verlag GmbH ISBNs: 3-527-30372-3 (Softcover); 3-527-60004-3 (Electronic) 3 The Electron Density as the Basic Variable: Early Attempts In this section we will approach the question which is at the very heart of density functional theory: can we possibly replace the complicated N-electron wave function with its dependence on 3N spatial plus N spin variables by a simpler quantity, such as the electron density?
These indirect contributions can get quite significant and in some cases even constitute the decisive part of E HF C (Baerends and Gritsenko, 1997). 5 Electron Correlation point, but that there are also some significant differences. Some quantitative data to corroborate the statements of this section can be found in Table 5-1. In the context of traditional wave function based ab initio quantum chemistry a large variety of computational schemes to deal with the electron correlation problem has been devised during the years.
A Chemists Guide to Density Functional Theory by Holtje, Hans-Dieter